What normal to the curve `y=x^2` forms the shortest chord?

The equation of the normal to the curve y=2x^3+6x^2-9 where the curve crosses the y-axis is

Slope of normal to the curve y=x^2-x and x=2 is

The equation of normal to the curve y=6-x^(2), where the normal is parallel to the line x-4y+3=0 is

The equation of the normal to the curve y=x(2-x) at the point (2, 0) is

Equation of the normal to the curve y=-sqrt(x)+2 at the point of its intersection with the curve y=tan(tan-1x) is

The equation of normal to the curve y^(2)=8x is

What is the slope of the normal to the curve y=2x^(2) + 3 sin x at x = 0?

The equation of the normal to the curve 2y=3-x^2 at (1,1) is